A SIEVE STOCHASTIC GRADIENT DESCENT ESTIMATOR FOR ONLINE NONPARAMETRIC REGRESSION IN SOBOLEV ELLIPSOIDS.

ABSTRACT: The goal of regression is to recover an unknown underlying function that best links a set of predictors to an outcome from noisy observations. in nonparametric regression, one assumes that the regression function belongs to a pre-specified infinite-dimensional function space (the hypothesis space). in the online setting, when the observations come in a stream, it is computationally-preferable to iteratively update an estimate rather than refitting an entire model repeatedly. inspired by nonparametric sieve estimation and stochastic approximation methods, we propose a sieve stochastic gradient descent estimator (Sieve-SGD) when the hypothesis space is a Sobolev ellipsoid. We show that Sieve-SGD has rate-optimal mean squared error (MSE) under a set of simple and direct conditions. The propos

SUBMITTER: Zhang T 

PROVIDER: S-EPMC10760996 | biostudies-literature | 2022 Oct

REPOSITORIES: biostudies-literature